An injection-molding machine provided with such a take-off member has been disclosed in commonly owned U.S. Pat. Nos. 3,454,991 and 3,700,375. The mechanism described in these patents includes a cam and a cam follower respectively mounted on the two mold portions in order to correlate the insertion and retraction of the take-off member with the relative displacement of the mold-carrying platens. Such a camming mechanism, which positively prevents any malfunction due to premature closure of the mold or to a delayed retraction of the take-off member, is practical only with machines having a relatively short mold-opening stroke. With elongate workpieces, such as vials or bottle preforms, the equipment tends to become unduly cumbersome.